PGFPlots linear regression variance

Question

I would like to compute a weighted linear regression of my data, but my data file lists the standard deviation of each point, not the variance.

Is there a way to have an equation in the variance to square my standard deviation? I will be reading my data in from a file.

I have seen the following in the PGFPlotsTable manual, but can't make it work in my instance. I've altered it to do what I want it to do.

\pgfplotstableset{
   create on use/vari/.style={
      create col/expr={U^2}}
}

My file:

\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfplotstable}

\begin{document}


\begin{tikzpicture}[baseline]
\begin{axis}[
    xlabel={$x$},
    ylabel={$y$},
]
\addplot[   
    only marks,
    error bars/.cd, y dir=both, y explicit,
] 
table[
    x = X,
    y = Y,
    y error = U,
]
{
X   Y   U 
1   1   1       
20  20  4.472   
40  35  5.916       
60  71  8.426
80  78  8.832
100 114 10.677  
};

\addplot[
    red,
]
table[
    x = X,
    y = {create col/linear regression={y=Y, variance=U}}, %this should be U^2
]
{
X   Y   U
1   1   1       
20  20  4.472   
40  35  5.916       
60  71  8.426
80  78  8.832
100 114 10.677  
};
\end{axis}
\end{tikzpicture}

\end{document}

Answer 1

You are very nearly there. All that's missing is to use \thisrow{U} instead of U in your create col/expr

\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfplotstable}

\begin{document}
\pgfplotstabletypeset[ % just to show that this works
   create on use/vari/.style={
      create col/expr={\thisrow{U}^2}},
   columns={U,vari}
]{
X   Y   U 
1   1   1       
20  20  4.472   
40  35  5.916       
60  71  8.426
80  78  8.832
100 114 10.677  
}

\bigskip

\begin{tikzpicture}[baseline]
\begin{axis}[
    xlabel={$x$},
    ylabel={$y$},
]
\addplot[   
    only marks,
    error bars/.cd, y dir=both, y explicit,
] 
table[
    x = X,
    y = Y,
    y error = U,
]
{
X   Y   U 
1   1   1       
20  20  4.472   
40  35  5.916       
60  71  8.426
80  78  8.832
100 114 10.677  
};

\addplot[
    red,
]
table[
    create on use/vari/.style={
      create col/expr={\thisrow{U}^2}},
    x = X,
    y = {create col/linear regression={y=Y, variance=vari}}, %this should be U^2
]
{
X   Y   U
1   1   1       
20  20  4.472   
40  35  5.916       
60  71  8.426
80  78  8.832
100 114 10.677  
};
\end{axis}
\end{tikzpicture}

\end{document}